T-shirt: an informal shirt with short sleeves and no collar or buttons, or just a few buttons at the top
But, what to call "a T-shirt without sleeves" like this:
[vest] 1 /vest/ ●●○ noun [countable]
1 British English a piece of underwear without sleeves that you wear on the top half of your body SYN undershirt American English
But a child can wear a vest when they go out.